Laws of motion practice · Mixed difficulty

Assertion :- Mountain roads rarely go straight up the slope.

Reason :- Slope of mountains are large, therefore more chances of vehicle to slip from roads.

A man of 50 kg is standing at one end on a boat of length 25 m and mass 200 kg. If he starts running and when he reaches the other end, he has a velocity $2\;\mathrm{m}{\mathrm{s}^{ - 1}}$ with respect to the boat. The final velocity of the boat is ( in $\mathrm{m}{\mathrm{s}^{ - 1}})$

Statement-I: When a person is on the floor of a lift which is at rest, the resultant force on him is equal to his weight
Statement-II: When the lift is moving with uniform velocity, then the apparent weight of the man is zero

Assertion: Sum of work done by the Newton’s third law pair internal forces, acting between two particles may be zero.
Reason: If two particles undergo same displacement then work done by Newton’s third law pair forces on them is of opposite sign and equal magnitude.

Which of the following statement is correct for friction?

Statement-I: When a person walks on a rough surface, the frictional force exerted by surface on the person is opposite to the direction of his motion.
Statement-II: It is the force exerted by the road on the person that causes the motion.

The retarding acceleration of $7.35 \mathrm{~m} \mathrm{s}^{-2}$ due to frictional force stops the car of mass 400 kg travelling on a road. The coefficient of friction between the tyre of the car and the road is

Assertion $[A]$ : A boy feels more pain when he falls down on a hard concrete floor than when he falls on the sand floor

Reason $[R]$: Every action has equal and opposite reaction. The time of impact of cement floor is smaller compared to that of sand floor

Five forces inclined at an angle of $72^{\circ}$ w.r.t. each other act on a particle of mass $m$ placed at the origin. Four forces are of magnitude $F_1$ and one has a magnitude $F_2$. Find the resultant acceleration of the particle.

The breaking strength of the cable used to pull a body is $40 \mathrm{~N}$. A body of mass $8 \mathrm{~kg}$ is resting on a table of coefficient of friction $\mu=0.2$ The maximum acceleration which can be peoduced by the cable connected to the body is (Take, $g=10 \mathrm{~ms}^{-2}$)

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

A stick of 1 m is moving with velocity of $2.7 \times {10^8}\;m{s^{ - 1}}$. What is the apparent length of the stick $\left( {c = 3 \times {{10}^8}\;m{s^{ - 1}}} \right)$

A cyclist is speeding at $20 \mathrm{~m} / \mathrm{s}$ on a level road taking a level circular turn of radius $200 \mathrm{~m}$ without reducing speed. What is minimum coefficient of static friction required between tyres and road so that cyclist take turn without slipping?

A trolley filled with sand moves on a smooth horizontal surface with a velocity ${V}_{{0}}$. A small hole is made at the base of it from which sand is leaking out vertically down at constant rate. As the sand leaks out
a) The velocity of the trolley remains constant
b) The velocity of the trolley increases
c) The velocity of trolley decreases
d) The momentum of trolley + leaked out sand is conserved

(A): A sphere cannot roll on a smooth inclined surface.
(R): For a smooth inclined surface force of friction is equal to zero.

A bullet hits and gets embedded in a solid block resting on a frictionless surface .In this process which one of the following is correct?

Assertion: Static friction is a force which can be self-adjusted up to its limit $\mu_{{s}} {N}$ where $\mu_{{s}}$ is the co-efficient of static friction.
Reason: The equation $f_s=\mu_s N$ is applicable only when the maximum value of static friction comes into play.

An electric fan is placed on a stationary boat
and air is blown with it on the sail of the boat.
Which of the following statements is correct?

Which of the following statements is/are correct about action and reaction forces?
I. Action and reaction are simultancous forces
II. There is no cause-effect relation between action and reaction.
III. Action and reaction always on two different body

A rectangular wooden box $10 \mathrm{~cm} \times 20 \mathrm{~cm} \times 40 \mathrm{~cm}$ in size is kept on a horizontal surface with its face of largest area on the surface. A minimum force of $10 \mathrm{~N}$ applied parallel to the surface sets the box in sliding motion along the surface. If the box is now kept with its face of smaller area in contact with the surface, the minimum force applied parallel to the surface, to set the box in motion, is

The coefficient of static friction between two surfaces depends upon

A block has been placed on an inclined plane with the slope
angle $\theta,$ block slides down the plane at constant speed. The
coefficient of kinetic friction is equal to

A sphere cannot roll without applying external force on

Three concurrent co-planar forces 1 N,2 N and 3 N acting along different directions on a body

The two factors on which the momentum of a body depends are_____ and _____

1 kg body explodes into three fragments. The ratio of their masses is $1:1:3$. The fragments of same mass move perpendicular to each other with speeds $\;30\mathrm{m}{\mathrm{s}^{ - 1}}$, while the heavier part remains in the initial direction. The speed of heavier part is

Tension in the cable supporting an elevator, is equal to the weight of the elevator. From this, we can conclude that the elevator is going up or down with a

Which one of the following is not a contact force?

When the speed of a moving body is doubled

Statement-I: Shock absorbers reduce the magnitude of change in momentum.
Statement-II: Shock absorbers increase the time of action of impulsive force.